Dissipativity and Optimal Control: Examining the Turnpike Phenomenon

This article describes the manifold relationships dissipativity and optimal control, with a focus on recent developments. In the early days of dissipativity theory, the questions “how can optimal control be used to establish dissipativity?” and vice versa, “how can dissipativity can be used to establish (inverse) optimality?” were extensively investigated. Recently, the question “what does dissipativity tell us about the qualitative behavior of optimally controlled systems?” came into focus. This development was triggered by the observation that dissipativity is extremely useful for the understanding of (economic) model predictive control schemes, and opened a new view on the relationship between dissipativity and optimal control.